Not just private packs, but I'd suggest there be a right-click menu to remove any pack. It could show "Install pack..." or "Uninstall pack..." depending on the state. And maybe also "Show folder" although I personally don't know how to do that cross-platform without looking into it.
Unrelated, but it also wouldn't be a bad idea to have a "cancel" button on the pack download dialog, and to make the dialog unable to be closed, because it currently breaks the launcher if you try to abort.
I suppose I could add these things myself and see how it turns out.